报告题目：Zauner’s Conjecture: Fiducial States in Vector Spaces

报告时间：2023-11-17   16:00-17:00

报 告 人 ：骆顺龙 研究员  中国科学院数学与系统科学研究院

报告地点：老外楼概率统计系办公室

Abstract：In the stabilizer formalism of quantum theory, stabilizer states serves as classical objects, and non-stabilizer states (magic states) are resource for genuine quantum computation. In the paradigm of quantum measurement, symmetric informationally complete positive operator valued measures (SICs) play a prominent role due to their structural symmetry and remarkable features. However, their existence in all dimensions, although strongly supported by a plethora of theoretical and numerical evidence, remains an elusive open problem (Zauner'sconjecture). A standard method for constructing SICs is via the orbit of Heisenberg-Weyl group on a fiducial state. A natural question arises as the relation between stabilizer states and fiducial states. In this talk, we connect them by showing that they are on two extremes with respect to the p-norm of characteristic functions of quantum states. This not only reveals a simple path from stabilizer states to SIC fiducial states which shows in a quantitative fashion that they are as far away as possible from each other, but also provides a simple reformulation of Zauner'sconjecture. A convenient criterion for non-stabilizernessand some open problems are also presented.